If the Republicans quit, refuse to do a deal in the face of what looks like the president being so willing to compromise that he is damaging his reputation with his own party, they will look like ideological hotheads.

Just to make sure they are put on the spot the president has laced his package with tax increases, which he knows are anathema to most Republicans.

This may not work. The public may decide the Republicans are the ones being reasonable, that the president's proposed cuts are not big enough or even that the debt ceiling shouldn't be raised anyhow.

But the stakes are high. Mr Obama was elected in part on the big cuddly vision of bringing all sides together, to ending Washington politics as usual. That clearly hasn't happened.

So he has to have a story to explain why red and blue has not merged into a consensual purple. Indeed since he took office the gap between Republicans and Democrats has widened.

His latest offer of cuts is designed to make a specific argument - that he is willing to go the extra mile, to stick his neck out, but that his opponents are so entrenched in their narrow political foxhole that they would rather cause another economic crisis than make a single compromise.